A Finite Volume Method Based on the Constrained Nonconforming Rotated Q1-Constant Element for the Stokes Problem

We construct a finite volume element method based on the constrained nonconforming rotated Q₁-constant element (CNRQ₁-P₀) for the Stokes problem. Two meshes are needed, which are the primal mesh and the dual mesh. We approximate the velocity by CNRQ₁ elements and the pressure by piecewise constants. The errors for the velocity in the H¹ norm and for the pressure in the L² norm are O(h) and the error for the velocity in the L² norm is O(h²). Numerical experiments are presented to support our theoretical results.     

一类带扰动的Sine-Gordon方程的谱方法

研究一类具扰动的Sine-Gordon方程u_tt-u_xx+αsinu-βu_xxt=g(u),t>0,-∞< x< ∞的周期初值问题,提出了谱方法,并用先验估计方法作了误差估计,证明了近似方法的收敛性,并得到了该问题广义解的存在、唯一性。     

Suppressing the mechanical quadrature error of a quartz double-H gyroscope through laser trimming

In this paper,we introduce a z-axis quartz gyroscope using a double-H tuning fork,which has a high sensitivity.However,it also causes a large mechanical quadrature error.The laser trimming method is used to suppress this error at quartz level.The trimming law is obtained through the finite element method(FEM).A femtosecond laser processing system is used to trim the gold balancing masses on the beams,and experimental results are basically consistent with the simulated ones.The mechanical quadrature error is suppressed by 96%,from 26.3°s-1 to 1.1°s-1.Nonlinearity changes from 1.48%to 0.30%,angular random walk(ARW)is reduced from 2.19°h-1/2 to 1.42°h-1/2,and bias instability is improved by a factor of 7.7,from 197.6°h-1 to 25.4°h-1.     

A design of novel photonic crystal fiber with low and flattened dispersion for supporting 84 orbital angular momentum modes

A dual-guided photonic crystal fiber(PCF) with low and flattened dispersion is designed, which can support a large number of orbital angular momentum(OAM) modes. The properties of the proposed PCF are systematically analyzed through the finite element method. The results show that the proposed PCF can support up to 84 OAM modes with 600 nm bandwidth ranging from 1000 to1600 nm. All values of mode purity are above 91.7%, the isolation parameters are larger than 67 dB and the maximum value up to 145 dB, the lowest confinement loss is only 5×10~(-13) dB·m~(-1).More importantly, the values of dispersion for all modes are less than 40 ps·km~(-1)·nm~(-1), and the lowest dispersion variation is only 0.7 ps·km~(-1)·nm~(-1). These superior optical properties make the proposed PCF have great advantage in stable transmissions of data and long-distance optical fiber communication system with large capacity.     

ICP-AES法测定石膏中的多元素含量

分别采用酸溶和碱熔两种样品前处理方法处理样品,ICP-AES测定石膏中多元素。酸溶法适用于样品中CaO,SO₃,Al₂O₃,Fe₂O₃,MgO,K₂O,Na₂O,TiO₂,P₂O₅,MnO,SrO,BaO的同时测定。碱熔法适用于样品中CaO,SO₃,SiO₂,Al₂O₃,Fe₂O₃,MgO,TiO₂,P₂O₅,MnO,SrO,BaO,B₂O₃的同时测定。根据各个元素的性质、含量高低和基体因素配制了不同的系列标准溶液,确定了各个元素的最佳分析谱线和相应分析谱线下方法的检出限和定量限。结果表明,除酸溶法测定TiO₂的回收率略低外(81%～87%),两种前处理方法测定石膏样品中各元素的整体回收率为93%～110%,RSD(n=6)为0.70%～3.42%。但CaO和SO₃测定的准确度还比不上化学分析方法。采用本方法测定石膏中的CaO和SO₃仅适用于对测定结果准确度要求相对较低的情况。本方法操作简单,分析速度快,测定结果可靠,可以同时测定石膏中的多元素,综合酸溶和碱熔两种处理方法,可以实现石膏样品的全元素分析。     

An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations

In the paper, an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.     

QEPAS系统中石英音叉模态仿真计算与研究

对石英音叉增强型光声光谱(QEPAS)系统中常用的石英音叉进行了有限元模态计算，获得石英音叉前6阶振型与模态频率，认知了第4阶对称摆动振型为有效振动，利用单因素法分析了石英音叉的音臂长度l₁、音臂宽度w₁、音臂厚度t、音臂切角θ、音臂圆孔直径d及音臂圆孔高度h对低阶有效共振频率(Fre)的影响，敏感度依次为： l₁> w₁>d>θ>t>h，考虑实际设计情形，筛选出了l₁，w₁，d与h四个石英音叉设计变量，采用Box-Behnken实验设计方案与RSM(response surface methodology)方法，以Fre为函数目标，建立l₁，w₁，d与h的二次回归响应面模型，得到了参数之间的交互作用，利用Design-Expert软件对响应面模型进行设计参数反求，结果表明，在15 000 Hz≤Fre≤25 000 Hz计算区域内误差较小，基本满足QEPAS系统的计算需求，所提出的研究与设计方法具有一定通用性，可为QEPAS系统中石英音叉结构参数设计提供参考。     

抛物方程基于自然边界归化的耦合法

将冯康和余德浩提出的自然边界归化方法^[1~4]应用于求解抛物方程初边值外区域问题,提出一种自然边界元与有限元耦合算法。先将控制方程对时间进行离散化,得到关于时间步长的离散化格式,给出圆外域上的自然积分方程,基于此研究抛物方程无界区域问题的自然边界元与有限元耦合法,最后给出相应的数值例子。     

有限体积元数值方法在大气污染模式中的应用

运用有限体积元方法分析求解大气污染模型问题,分别选取试探函数空间和检验函数空间为一次元函数空间和分片常数函数空间,并且给出L²估计和H¹估计,通过数值实验与有限差分方法进行分析与比较,说明其有效性.为改善大气污染问题的模拟提供实用有效的方法.     

基于多峰协同和纯元素特征峰面积归一化的重叠峰快速解析算法

由于元素间特征峰的相互干扰,受实验仪器能量分辨率的影响,当多个元素的特征峰峰位相近且展宽较宽时就会形成重叠峰。以分离度低且分解需求精度高的重叠峰为研究对象,提出一种基于多峰协同和纯元素特征峰面积归一化的重叠峰快速解析算法,并结合实际的X射线荧光光谱进行了新方法的验证。选取镝铁合金的X射线荧光光谱图作为实例,在该实验条件下镝L_α特征峰和铁K_α特征峰形成的重叠峰分离度约为0.273 5,同时还存在分离度较大但荧光产额较低的镝L_β特征峰和铁K_β特征峰。首先,配置浓度范围(7.8～8.2 mg·mL^-1)的镝标液和浓度范围(1.8～2.2 mg·mL^-1)的铁标液进行测量获取到纯元素谱图,分别进行面积归一化处理并取平均得到镝L_α峰和铁K_α峰的归一化特征峰。然后,使用镝、铁标液混兑出铁元素质量百分比范围在19.1%～21%,梯度为0.1%的20组样品液进行测量。由于重叠峰部分仅由镝L_α峰和铁K     

NaGdF4纳米晶多元醇法的合成、表征与NaGdF4：Eu3+和NaGdF4：Yb3+, Er3+纳米晶的发光

通过多元醇法(polyol method)合成出NaGdF₄:Eu³⁺和NaGdF₄:Yb³⁺,Er³⁺纳米晶,利用X射线衍射(XRD)、场发射扫描电镜(FE-SEM)和傅立叶变换红外吸收光谱(FT-IR)对合成的样品进行了表征。研究了Eu³⁺掺杂样品的下转换发光和Yb³⁺/Er³⁺共掺杂样品的上转换发光。对未经退火和经过退火的样品进行了比较。     

低损耗低非线性高负色散光子晶体光纤的优化设计

设计了一种同轴双芯六角点阵光子晶体光纤, 该光纤中心缺失一根空气柱形成内纤芯, 通过减小第4环空气孔的直径形成外纤芯. 采用全矢量有限元法并结合各向异性完美匹配层边界条件, 对其色散、非线性、约束损耗和模场等特性进行了数值模拟. 结果发现, 该光纤呈现高负色散可调效应和较强的模场约束能力, 约束损耗接近10^-2 dB· m^-1. 调整光纤结构参数(即空气孔间隔Λ, 小孔直径d₁和相对孔间隔比f), 可以控制其高负色散工作波长. 若调整光纤结构参数Λ=1.2 μ, f=0.917, d₁=0.515 μm时, 该光纤在低损耗通信窗口C波段呈现负色散和负色散斜率, 其色散斜率在-1----6 ps· km^-1nm^-2范围内波动, 在波长1.55 μm处负色散值为-3400 ps· km^-1nm^-1, 模场面积高达43 μm², 非线性系数仅有3.6 km^-1W^-1. 该光纤在C波段呈现的低损耗低非线性高负色散特性, 具有很好的色散补偿能力, 将在长距离大容量 高功率高速光通信系统中获得很好的应用.     

Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions

In this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.     

一种新型高双折射光子晶体光纤特性研究

设计了一种高双折射高非线性光子晶体光纤, 采用全矢量有限元法研究了这种光纤的基模模场、双折射、非线性、有效模面积及色散特性. 数值研究发现, 减小孔间距Λ的大小, 在波长1550 nm 处, 该光纤可获得10^-2 数量级的双折射B, 比普通的椭圆保偏光纤高约两个数量级; 同时, 该光纤可获得42 W^-1·km^-1 的高非线性系数γ. 另外,分别在可见光和近红外波段出现了两个零色散波长, 在波长800–2000 nm 之间具有良好的色散平坦特性. 这种设计为获得高双折射高非线性超平坦色散光子晶体光纤提供了一种新的方法, 该光纤在偏振控制、非线性光学和色散控制方面具有广泛的应用前景. 关键词： 光子晶体光纤 高双折射 高非线性 有限元法     

Phantom and in vivo study of the Look-Locher T1 mapping method

This paper describes and tests the LL-EPI method for obtaining quantitative T₁ estimates in a few seconds thereby allowing dynamic T₁ studies. It is shown that the method works even when there is an inflow into the imaged volume, e.g., in a vessel. No calibration is needed. The method has been tested in a phantom study with several different scan parameter set-ups, with and without inflow. The method shows robustness and individual scan parameters and inflow rates do not influence the ability to calculate the Gd-DTPA concentration. Linearity prevail between the measured 1/T₁ and the Gd-DTPA concentration in the range 150 < T₁ < 2500 ms. In a dynamic Gd-DTPA phantom study, it was shown that the dynamic LL-EPI T₁ mapping technique was three times more sensitive than the signal from a T^*₂-weighted EPI sequence. In an in vivo study, dynamic T₁ mapping of the Gd-DTPA uptake in a meningioma was performed. Inspection of the uptake curves indicates that the method is feasible in clinical perfusion studies.     

氦原子1s2p态的有限元近似能量

用有限元方法近似计算了1s2p态氦原子单态和三重态的能量,所得结果的相对误差:三重态为10^-6,单态为10^-4.这一结果比Schertzer^[1]对基态氦原子的相应结果稍好.有限元法导致的大型广义矩阵特征值问题,对于基态是对称的,而对于1s2p态是非对称的,给求解带来了难度.由波函数的图形说明,在有界区域上求Schrödinger方程的近似解是合理的.     

Exact Solutions of the φ^6 ＋ φ^5 Model Using Truncated Method

In this letter, the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions can be solved by a truncated series method. A series of solitary solutions of the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions have be obtained.     

Application of activation radiography in experimental investigation

A method of neutron activation radiography has been elaborated based on the neutron irradiation of the sample under study and subsequent photoregistration of the induced activity of the given element. The method is intended for investigation of spatial distributions of gold and other elements in various substances. Principal factors such as spatial resolution, range of local detection limit, as well as optimal regimes of irradiation, cooling and photoexposure are estimated. These factors determine the conditions to be provided to obtain selective radiograms.

Radiographic methods for investigation of the distributions of more than 40 elements with local detection limits within the range from 10⁻³ to 10⁻⁸ g · mm⁻² and resolution of 1 – 100 μm have also been developed.

Methods elaborated for analysis of geological and geochemical samples produce representative data on the regularities of element spread in the minerals and samples of ores and holding rocks.     

High-precision image position sensing methods suitable for 3-D measurement

A high-precision image position sensing method for a position sensitive detector (PSD) with a kaleidoscopic mirror tunnel (KM-PSM) is introduced. In order to increase the relative resolution of the image position detecting element itself, a hybrid type position sensitive device (R-HPSD) has been invented. A 1-D mark direction sensing method (PM-DSM) which consists of a 1-D image position sensing element, a cylindrical lens and a parallel mirror tunnel is proposed for the realization of a high-precision and miniaturized 3-D position measuring system. Furthermore, an optical range sensing method (RORS), which is suitable for realizing a miniaturized optical range sensing probe based on the triangulation, is proposed.     

Configuration interaction studies on the spectroscopic properties of PbO including spin-orbit coupling

Lead oxide(Pb O), which plays the key roles in a range of research fields, has received a great deal of attention. Owing to the large density of electronic states and heavy atom Pb including in Pb O, the excited states of the molecule have not been well studied. In this work, high level multireference configuration interaction calculations on the low-lying states of Pb O have been carried out by utilizing the relativistic effective core potential. The effects of the core-valence correlation correction, the Davidson modification, and the spin–orbital coupling on the electronic structure of the Pb O molecule are estimated. The potential energy curves of 18 Λ-S states correlated to the lowest dissociation limit(Pb(~3P_g) + O(~3P_g)) are reported. The calculated spectroscopic parameters of the electronic states below 30000 cm~(-1), for instance, X~1Σ~+, 1~3Σ~+,and 1~3Σ~-, and their spin–orbit coupling interaction, are compared with the experimental results, and good agreements are derived. The dipole moments of the 18 Λ-S states are computed with the configuration interaction method, and the calculated dipole moments of X~1Σ~+and 1~3Σ~+are consistent with the previous experimental results. The transition dipole moments from 1~1Π, 2~1Π, and 2~Σ to X~1Σ~+and other singlet excited states are estimated. The radiative lifetime of several low-lying vibrational levels of 1~1Π, 2~1Π, and 2~1Σ~+ states are evaluated.